I don't think the bolded is actually a concern. When fully healthy, our top-12 has Kane, Hyman, Draisaitl, Puljujarvi, Foegele, Archibald, and Kassian as far as big and/or physical guys go. 5 of those guys play in the top-9. McDavid, RNH, McLeod, and Yamamoto are the only top-9 players who don't fit that list, so unless we're trading Yams or moving McLeod to the 4th line, there's not really any room for another big guy in the top-9.
Only Kane brings a physical intimidation element and willingness to get in opposing player's faces. Kassian is a liability on the ice, Archibald is useless with the covid rules, Hyman/Foegele/Pulj/Drai rarely initiate anything(Drai might be the biggest goon of the 4 of them).
When it comes to grit and drive, along with the willingness to initiate contact, the Oilers are pretty soft throughout the roster. Kane even pointed it out not long after he got here, he himself being a major addition to try and rectify the Oiler's tendency towards passive perimeter play.